LMFDB - Embedded newform 6017.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42329 q^{2} -0.918445 q^{3} +3.87233 q^{4} -2.10804 q^{5} +2.22566 q^{6} -2.69568 q^{7} -4.53719 q^{8} -2.15646 q^{9} +O(q^{10})$	\(q-2.42329 q^{2} -0.918445 q^{3} +3.87233 q^{4} -2.10804 q^{5} +2.22566 q^{6} -2.69568 q^{7} -4.53719 q^{8} -2.15646 q^{9} +5.10839 q^{10} +1.00000 q^{11} -3.55652 q^{12} -1.31790 q^{13} +6.53241 q^{14} +1.93612 q^{15} +3.25026 q^{16} -1.02624 q^{17} +5.22572 q^{18} +1.40367 q^{19} -8.16302 q^{20} +2.47583 q^{21} -2.42329 q^{22} -7.47517 q^{23} +4.16716 q^{24} -0.556169 q^{25} +3.19364 q^{26} +4.73592 q^{27} -10.4386 q^{28} +4.75007 q^{29} -4.69177 q^{30} +4.78215 q^{31} +1.19805 q^{32} -0.918445 q^{33} +2.48687 q^{34} +5.68260 q^{35} -8.35052 q^{36} -7.86278 q^{37} -3.40149 q^{38} +1.21042 q^{39} +9.56457 q^{40} +8.85425 q^{41} -5.99966 q^{42} -3.78885 q^{43} +3.87233 q^{44} +4.54590 q^{45} +18.1145 q^{46} -12.0893 q^{47} -2.98519 q^{48} +0.266696 q^{49} +1.34776 q^{50} +0.942544 q^{51} -5.10333 q^{52} +3.68886 q^{53} -11.4765 q^{54} -2.10804 q^{55} +12.2308 q^{56} -1.28919 q^{57} -11.5108 q^{58} +7.33831 q^{59} +7.49728 q^{60} +3.68949 q^{61} -11.5885 q^{62} +5.81313 q^{63} -9.40375 q^{64} +2.77818 q^{65} +2.22566 q^{66} -3.00896 q^{67} -3.97393 q^{68} +6.86553 q^{69} -13.7706 q^{70} +4.85676 q^{71} +9.78426 q^{72} +13.9945 q^{73} +19.0538 q^{74} +0.510810 q^{75} +5.43546 q^{76} -2.69568 q^{77} -2.93319 q^{78} -11.2438 q^{79} -6.85168 q^{80} +2.11969 q^{81} -21.4564 q^{82} +15.9306 q^{83} +9.58724 q^{84} +2.16335 q^{85} +9.18148 q^{86} -4.36268 q^{87} -4.53719 q^{88} +8.85401 q^{89} -11.0160 q^{90} +3.55263 q^{91} -28.9463 q^{92} -4.39214 q^{93} +29.2958 q^{94} -2.95899 q^{95} -1.10034 q^{96} +6.42119 q^{97} -0.646282 q^{98} -2.15646 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.42329	−1.71352	−0.856762	−	0.515712i	$-0.827527\pi$
$2$	−2.42329	−1.71352	−0.856762	+	0.515712i	$0.827527\pi$
$3$	−0.918445	−0.530264	−0.265132	−	0.964212i	$-0.585416\pi$
$3$	−0.918445	−0.530264	−0.265132	+	0.964212i	$0.585416\pi$
$4$	3.87233	1.93616
$5$	−2.10804	−0.942744	−0.471372	−	0.881934i	$-0.656241\pi$
$5$	−2.10804	−0.942744	−0.471372	+	0.881934i	$0.656241\pi$
$6$	2.22566	0.908621
$7$	−2.69568	−1.01887	−0.509436	−	0.860509i	$-0.670146\pi$
$7$	−2.69568	−1.01887	−0.509436	+	0.860509i	$0.670146\pi$
$8$	−4.53719	−1.60414
$9$	−2.15646	−0.718820
$10$	5.10839	1.61541
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.55652	−1.02668
$13$	−1.31790	−0.365519	−0.182759	−	0.983158i	$-0.558503\pi$
$13$	−1.31790	−0.365519	−0.182759	+	0.983158i	$0.558503\pi$
$14$	6.53241	1.74586
$15$	1.93612	0.499904
$16$	3.25026	0.812566
$17$	−1.02624	−0.248900	−0.124450	−	0.992226i	$-0.539717\pi$
$17$	−1.02624	−0.248900	−0.124450	+	0.992226i	$0.539717\pi$
$18$	5.22572	1.23171
$19$	1.40367	0.322023	0.161012	−	0.986953i	$-0.448524\pi$
$19$	1.40367	0.322023	0.161012	+	0.986953i	$0.448524\pi$
$20$	−8.16302	−1.82531
$21$	2.47583	0.540271
$22$	−2.42329	−0.516647
$23$	−7.47517	−1.55868	−0.779340	−	0.626601i	$-0.784445\pi$
$23$	−7.47517	−1.55868	−0.779340	+	0.626601i	$0.784445\pi$
$24$	4.16716	0.850618
$25$	−0.556169	−0.111234
$26$	3.19364	0.626325
$27$	4.73592	0.911429
$28$	−10.4386	−1.97270
$29$	4.75007	0.882066	0.441033	−	0.897491i	$-0.354612\pi$
$29$	4.75007	0.882066	0.441033	+	0.897491i	$0.354612\pi$
$30$	−4.69177	−0.856597
$31$	4.78215	0.858899	0.429450	−	0.903091i	$-0.358708\pi$
$31$	4.78215	0.858899	0.429450	+	0.903091i	$0.358708\pi$
$32$	1.19805	0.211788
$33$	−0.918445	−0.159881
$34$	2.48687	0.426495
$35$	5.68260	0.960535
$36$	−8.35052	−1.39175
$37$	−7.86278	−1.29263	−0.646317	−	0.763069i	$-0.723691\pi$
$37$	−7.86278	−1.29263	−0.646317	+	0.763069i	$0.723691\pi$
$38$	−3.40149	−0.551795
$39$	1.21042	0.193822
$40$	9.56457	1.51229
$41$	8.85425	1.38280	0.691401	−	0.722471i	$-0.256994\pi$
$41$	8.85425	1.38280	0.691401	+	0.722471i	$0.256994\pi$
$42$	−5.99966	−0.925768
$43$	−3.78885	−0.577794	−0.288897	−	0.957360i	$-0.593289\pi$
$43$	−3.78885	−0.577794	−0.288897	+	0.957360i	$0.593289\pi$
$44$	3.87233	0.583775
$45$	4.54590	0.677663
$46$	18.1145	2.67083
$47$	−12.0893	−1.76340	−0.881702	−	0.471807i	$-0.843602\pi$
$47$	−12.0893	−1.76340	−0.881702	+	0.471807i	$0.843602\pi$
$48$	−2.98519	−0.430875
$49$	0.266696	0.0380995
$50$	1.34776	0.190602
$51$	0.942544	0.131983
$52$	−5.10333	−0.707704
$53$	3.68886	0.506704	0.253352	−	0.967374i	$-0.418467\pi$
$53$	3.68886	0.506704	0.253352	+	0.967374i	$0.418467\pi$
$54$	−11.4765	−1.56175
$55$	−2.10804	−0.284248
$56$	12.2308	1.63441
$57$	−1.28919	−0.170758
$58$	−11.5108	−1.51144
$59$	7.33831	0.955366	0.477683	−	0.878532i	$-0.341477\pi$
$59$	7.33831	0.955366	0.477683	+	0.878532i	$0.341477\pi$
$60$	7.49728	0.967895
$61$	3.68949	0.472391	0.236195	−	0.971706i	$-0.424100\pi$
$61$	3.68949	0.472391	0.236195	+	0.971706i	$0.424100\pi$
$62$	−11.5885	−1.47174
$63$	5.81313	0.732385
$64$	−9.40375	−1.17547
$65$	2.77818	0.344591
$66$	2.22566	0.273959
$67$	−3.00896	−0.367603	−0.183801	−	0.982963i	$-0.558840\pi$
$67$	−3.00896	−0.367603	−0.183801	+	0.982963i	$0.558840\pi$
$68$	−3.97393	−0.481910
$69$	6.86553	0.826512
$70$	−13.7706	−1.64590
$71$	4.85676	0.576391	0.288196	−	0.957572i	$-0.406945\pi$
$71$	4.85676	0.576391	0.288196	+	0.957572i	$0.406945\pi$
$72$	9.78426	1.15309
$73$	13.9945	1.63794	0.818968	−	0.573839i	$-0.194546\pi$
$73$	13.9945	1.63794	0.818968	+	0.573839i	$0.194546\pi$
$74$	19.0538	2.21496
$75$	0.510810	0.0589833
$76$	5.43546	0.623490
$77$	−2.69568	−0.307201
$78$	−2.93319	−0.332118
$79$	−11.2438	−1.26503	−0.632516	−	0.774548i	$-0.717978\pi$
$79$	−11.2438	−1.26503	−0.632516	+	0.774548i	$0.717978\pi$
$80$	−6.85168	−0.766042
$81$	2.11969	0.235521
$82$	−21.4564	−2.36946
$83$	15.9306	1.74862	0.874308	−	0.485372i	$-0.161316\pi$
$83$	15.9306	1.74862	0.874308	+	0.485372i	$0.161316\pi$
$84$	9.58724	1.04605
$85$	2.16335	0.234649
$86$	9.18148	0.990064
$87$	−4.36268	−0.467728
$88$	−4.53719	−0.483666
$89$	8.85401	0.938524	0.469262	−	0.883059i	$-0.344520\pi$
$89$	8.85401	0.938524	0.469262	+	0.883059i	$0.344520\pi$
$90$	−11.0160	−1.16119
$91$	3.55263	0.372417
$92$	−28.9463	−3.01786
$93$	−4.39214	−0.455444
$94$	29.2958	3.02163
$95$	−2.95899	−0.303586
$96$	−1.10034	−0.112303
$97$	6.42119	0.651973	0.325987	−	0.945374i	$-0.394304\pi$
$97$	6.42119	0.651973	0.325987	+	0.945374i	$0.394304\pi$
$98$	−0.646282	−0.0652843
$99$	−2.15646	−0.216732
$100$	−2.15367	−0.215367
$101$	−15.5113	−1.54343	−0.771716	−	0.635968i	$-0.780601\pi$
$101$	−15.5113	−1.54343	−0.771716	+	0.635968i	$0.780601\pi$
$102$	−2.28406	−0.226155
$103$	11.6308	1.14602	0.573008	−	0.819549i	$-0.305776\pi$
$103$	11.6308	1.14602	0.573008	+	0.819549i	$0.305776\pi$
$104$	5.97955	0.586343
$105$	−5.21916	−0.509338
$106$	−8.93917	−0.868249
$107$	−15.2861	−1.47776	−0.738881	−	0.673836i	$-0.764646\pi$
$107$	−15.2861	−1.47776	−0.738881	+	0.673836i	$0.764646\pi$
$108$	18.3390	1.76468
$109$	−1.18087	−0.113107	−0.0565533	−	0.998400i	$-0.518011\pi$
$109$	−1.18087	−0.113107	−0.0565533	+	0.998400i	$0.518011\pi$
$110$	5.10839	0.487066
$111$	7.22153	0.685437
$112$	−8.76167	−0.827900
$113$	10.0801	0.948254	0.474127	−	0.880456i	$-0.342764\pi$
$113$	10.0801	0.948254	0.474127	+	0.880456i	$0.342764\pi$
$114$	3.12408	0.292597
$115$	15.7579	1.46944
$116$	18.3938	1.70782
$117$	2.84199	0.262742
$118$	−17.7828	−1.63704
$119$	2.76641	0.253597
$120$	−8.78453	−0.801915
$121$	1.00000	0.0909091
$122$	−8.94069	−0.809452
$123$	−8.13214	−0.733251
$124$	18.5180	1.66297
$125$	11.7126	1.04761
$126$	−14.0869	−1.25496
$127$	1.53610	0.136307	0.0681533	−	0.997675i	$-0.478289\pi$
$127$	1.53610	0.136307	0.0681533	+	0.997675i	$0.478289\pi$
$128$	20.3919	1.80241
$129$	3.47985	0.306384
$130$	−6.73233	−0.590464
$131$	1.09698	0.0958435	0.0479218	−	0.998851i	$-0.484740\pi$
$131$	1.09698	0.0958435	0.0479218	+	0.998851i	$0.484740\pi$
$132$	−3.55652	−0.309555
$133$	−3.78384	−0.328100
$134$	7.29157	0.629896
$135$	−9.98351	−0.859244
$136$	4.65624	0.399269
$137$	8.42685	0.719954	0.359977	−	0.932961i	$-0.382784\pi$
$137$	8.42685	0.719954	0.359977	+	0.932961i	$0.382784\pi$
$138$	−16.6372	−1.41625
$139$	−6.46863	−0.548662	−0.274331	−	0.961635i	$-0.588456\pi$
$139$	−6.46863	−0.548662	−0.274331	+	0.961635i	$0.588456\pi$
$140$	22.0049	1.85975
$141$	11.1033	0.935070
$142$	−11.7693	−0.987660
$143$	−1.31790	−0.110208
$144$	−7.00906	−0.584088
$145$	−10.0133	−0.831562
$146$	−33.9128	−2.80664
$147$	−0.244946	−0.0202028
$148$	−30.4473	−2.50275
$149$	7.03937	0.576688	0.288344	−	0.957527i	$-0.406895\pi$
$149$	7.03937	0.576688	0.288344	+	0.957527i	$0.406895\pi$
$150$	−1.23784	−0.101069
$151$	4.48252	0.364782	0.182391	−	0.983226i	$-0.441616\pi$
$151$	4.48252	0.364782	0.182391	+	0.983226i	$0.441616\pi$
$152$	−6.36870	−0.516570
$153$	2.21304	0.178914
$154$	6.53241	0.526397
$155$	−10.0810	−0.809722
$156$	4.68712	0.375270
$157$	−3.92980	−0.313632	−0.156816	−	0.987628i	$-0.550123\pi$
$157$	−3.92980	−0.313632	−0.156816	+	0.987628i	$0.550123\pi$
$158$	27.2471	2.16766
$159$	−3.38802	−0.268687
$160$	−2.52554	−0.199661
$161$	20.1507	1.58809
$162$	−5.13663	−0.403572
$163$	13.9010	1.08881	0.544406	−	0.838822i	$-0.316755\pi$
$163$	13.9010	1.08881	0.544406	+	0.838822i	$0.316755\pi$
$164$	34.2866	2.67733
$165$	1.93612	0.150727
$166$	−38.6046	−2.99629
$167$	1.96335	0.151929	0.0759645	−	0.997111i	$-0.475796\pi$
$167$	1.96335	0.151929	0.0759645	+	0.997111i	$0.475796\pi$
$168$	−11.2333	−0.866670
$169$	−11.2631	−0.866396
$170$	−5.24243	−0.402076
$171$	−3.02695	−0.231477
$172$	−14.6717	−1.11870
$173$	−8.60803	−0.654457	−0.327228	−	0.944945i	$-0.606115\pi$
$173$	−8.60803	−0.654457	−0.327228	+	0.944945i	$0.606115\pi$
$174$	10.5720	0.801463
$175$	1.49925	0.113333
$176$	3.25026	0.244998
$177$	−6.73983	−0.506597
$178$	−21.4558	−1.60818
$179$	15.5556	1.16268	0.581340	−	0.813660i	$-0.302528\pi$
$179$	15.5556	1.16268	0.581340	+	0.813660i	$0.302528\pi$
$180$	17.6032	1.31207
$181$	−8.95677	−0.665752	−0.332876	−	0.942971i	$-0.608019\pi$
$181$	−8.95677	−0.665752	−0.332876	+	0.942971i	$0.608019\pi$
$182$	−8.60904	−0.638145
$183$	−3.38859	−0.250492
$184$	33.9162	2.50034
$185$	16.5751	1.21862
$186$	10.6434	0.780414
$187$	−1.02624	−0.0750461
$188$	−46.8137	−3.41424
$189$	−12.7665	−0.928629
$190$	7.17048	0.520201
$191$	23.1298	1.67361	0.836806	−	0.547499i	$-0.184420\pi$
$191$	23.1298	1.67361	0.836806	+	0.547499i	$0.184420\pi$
$192$	8.63683	0.623309
$193$	−26.7959	−1.92881	−0.964405	−	0.264431i	$-0.914816\pi$
$193$	−26.7959	−1.92881	−0.964405	+	0.264431i	$0.914816\pi$
$194$	−15.5604	−1.11717
$195$	−2.55160	−0.182724
$196$	1.03273	0.0737668
$197$	−1.59916	−0.113935	−0.0569676	−	0.998376i	$-0.518143\pi$
$197$	−1.59916	−0.113935	−0.0569676	+	0.998376i	$0.518143\pi$
$198$	5.22572	0.371376
$199$	12.0933	0.857271	0.428636	−	0.903477i	$-0.358994\pi$
$199$	12.0933	0.857271	0.428636	+	0.903477i	$0.358994\pi$
$200$	2.52344	0.178434
$201$	2.76356	0.194927
$202$	37.5883	2.64471
$203$	−12.8047	−0.898712
$204$	3.64984	0.255540
$205$	−18.6651	−1.30363
$206$	−28.1848	−1.96373
$207$	16.1199	1.12041
$208$	−4.28351	−0.297008
$209$	1.40367	0.0970937
$210$	12.6475	0.872762
$211$	−8.61138	−0.592832	−0.296416	−	0.955059i	$-0.595791\pi$
$211$	−8.61138	−0.592832	−0.296416	+	0.955059i	$0.595791\pi$
$212$	14.2845	0.981062
$213$	−4.46066	−0.305640
$214$	37.0426	2.53218
$215$	7.98705	0.544712
$216$	−21.4878	−1.46206
$217$	−12.8911	−0.875108
$218$	2.86158	0.193811
$219$	−12.8532	−0.868539
$220$	−8.16302	−0.550351
$221$	1.35248	0.0909775
$222$	−17.4999	−1.17451
$223$	−5.52585	−0.370038	−0.185019	−	0.982735i	$-0.559235\pi$
$223$	−5.52585	−0.370038	−0.185019	+	0.982735i	$0.559235\pi$
$224$	−3.22956	−0.215784
$225$	1.19936	0.0799570
$226$	−24.4269	−1.62486
$227$	−7.32329	−0.486064	−0.243032	−	0.970018i	$-0.578142\pi$
$227$	−7.32329	−0.486064	−0.243032	+	0.970018i	$0.578142\pi$
$228$	−4.99217	−0.330614
$229$	−1.07543	−0.0710664	−0.0355332	−	0.999368i	$-0.511313\pi$
$229$	−1.07543	−0.0710664	−0.0355332	+	0.999368i	$0.511313\pi$
$230$	−38.1860	−2.51791
$231$	2.47583	0.162898
$232$	−21.5520	−1.41496
$233$	−1.67722	−0.109879	−0.0549393	−	0.998490i	$-0.517497\pi$
$233$	−1.67722	−0.109879	−0.0549393	+	0.998490i	$0.517497\pi$
$234$	−6.88696	−0.450215
$235$	25.4847	1.66244
$236$	28.4163	1.84975
$237$	10.3268	0.670801
$238$	−6.70382	−0.434544
$239$	−10.8477	−0.701682	−0.350841	−	0.936435i	$-0.614104\pi$
$239$	−10.8477	−0.701682	−0.350841	+	0.936435i	$0.614104\pi$
$240$	6.29289	0.406205
$241$	−7.48950	−0.482441	−0.241221	−	0.970470i	$-0.577548\pi$
$241$	−7.48950	−0.482441	−0.241221	+	0.970470i	$0.577548\pi$
$242$	−2.42329	−0.155775
$243$	−16.1546	−1.03632
$244$	14.2869	0.914625
$245$	−0.562206	−0.0359180
$246$	19.7065	1.25644
$247$	−1.84989	−0.117706
$248$	−21.6975	−1.37779
$249$	−14.6314	−0.927229
$250$	−28.3831	−1.79510
$251$	27.7115	1.74914	0.874568	−	0.484903i	$-0.161145\pi$
$251$	27.7115	1.74914	0.874568	+	0.484903i	$0.161145\pi$
$252$	22.5103	1.41802
$253$	−7.47517	−0.469960
$254$	−3.72241	−0.233565
$255$	−1.98692	−0.124426
$256$	−30.6080	−1.91300
$257$	9.95515	0.620985	0.310492	−	0.950576i	$-0.399506\pi$
$257$	9.95515	0.620985	0.310492	+	0.950576i	$0.399506\pi$
$258$	−8.43268	−0.524996
$259$	21.1956	1.31703
$260$	10.7580	0.667184
$261$	−10.2433	−0.634046
$262$	−2.65830	−0.164230
$263$	−17.1976	−1.06045	−0.530225	−	0.847857i	$-0.677892\pi$
$263$	−17.1976	−1.06045	−0.530225	+	0.847857i	$0.677892\pi$
$264$	4.16716	0.256471
$265$	−7.77627	−0.477692
$266$	9.16933	0.562208
$267$	−8.13192	−0.497666
$268$	−11.6517	−0.711739
$269$	−2.54516	−0.155181	−0.0775904	−	0.996985i	$-0.524723\pi$
$269$	−2.54516	−0.155181	−0.0775904	+	0.996985i	$0.524723\pi$
$270$	24.1929	1.47234
$271$	−2.92557	−0.177716	−0.0888580	−	0.996044i	$-0.528322\pi$
$271$	−2.92557	−0.177716	−0.0888580	+	0.996044i	$0.528322\pi$
$272$	−3.33555	−0.202247
$273$	−3.26289	−0.197479
$274$	−20.4207	−1.23366
$275$	−0.556169	−0.0335382
$276$	26.5856	1.60026
$277$	8.69420	0.522384	0.261192	−	0.965287i	$-0.415884\pi$
$277$	8.69420	0.522384	0.261192	+	0.965287i	$0.415884\pi$
$278$	15.6753	0.940145
$279$	−10.3125	−0.617394
$280$	−25.7830	−1.54083
$281$	23.3912	1.39540	0.697701	−	0.716389i	$-0.254207\pi$
$281$	23.3912	1.39540	0.697701	+	0.716389i	$0.254207\pi$
$282$	−26.9066	−1.60227
$283$	24.8099	1.47479	0.737397	−	0.675459i	$-0.236055\pi$
$283$	24.8099	1.47479	0.737397	+	0.675459i	$0.236055\pi$
$284$	18.8070	1.11599
$285$	2.71767	0.160981
$286$	3.19364	0.188844
$287$	−23.8682	−1.40890
$288$	−2.58355	−0.152237
$289$	−15.9468	−0.938049
$290$	24.2652	1.42490
$291$	−5.89751	−0.345718
$292$	54.1914	3.17131
$293$	9.94455	0.580967	0.290483	−	0.956880i	$-0.406184\pi$
$293$	9.94455	0.580967	0.290483	+	0.956880i	$0.406184\pi$
$294$	0.593574	0.0346180
$295$	−15.4694	−0.900666
$296$	35.6749	2.07356
$297$	4.73592	0.274806
$298$	−17.0584	−0.988168
$299$	9.85149	0.569727
$300$	1.97803	0.114201
$301$	10.2135	0.588698
$302$	−10.8624	−0.625063
$303$	14.2463	0.818427
$304$	4.56229	0.261665
$305$	−7.77759	−0.445343
$306$	−5.36284	−0.306573
$307$	11.2560	0.642414	0.321207	−	0.947009i	$-0.395912\pi$
$307$	11.2560	0.642414	0.321207	+	0.947009i	$0.395912\pi$
$308$	−10.4386	−0.594792
$309$	−10.6823	−0.607692
$310$	24.4291	1.38748
$311$	12.4455	0.705721	0.352861	−	0.935676i	$-0.385209\pi$
$311$	12.4455	0.705721	0.352861	+	0.935676i	$0.385209\pi$
$312$	−5.49188	−0.310917
$313$	−3.16794	−0.179062	−0.0895312	−	0.995984i	$-0.528537\pi$
$313$	−3.16794	−0.179062	−0.0895312	+	0.995984i	$0.528537\pi$
$314$	9.52305	0.537417
$315$	−12.2543	−0.690452
$316$	−43.5398	−2.44931
$317$	−2.69488	−0.151360	−0.0756798	−	0.997132i	$-0.524113\pi$
$317$	−2.69488	−0.151360	−0.0756798	+	0.997132i	$0.524113\pi$
$318$	8.21014	0.460402
$319$	4.75007	0.265953
$320$	19.8235	1.10817
$321$	14.0394	0.783605
$322$	−48.8309	−2.72124
$323$	−1.44050	−0.0801515
$324$	8.20814	0.456008
$325$	0.732973	0.0406580
$326$	−33.6862	−1.86571
$327$	1.08456	0.0599764
$328$	−40.1734	−2.21821
$329$	32.5889	1.79668
$330$	−4.69177	−0.258274
$331$	14.0372	0.771553	0.385777	−	0.922592i	$-0.373934\pi$
$331$	14.0372	0.771553	0.385777	+	0.922592i	$0.373934\pi$
$332$	61.6887	3.38561
$333$	16.9558	0.929170
$334$	−4.75777	−0.260334
$335$	6.34300	0.346555
$336$	8.04711	0.439006
$337$	21.0536	1.14686	0.573430	−	0.819255i	$-0.305612\pi$
$337$	21.0536	1.14686	0.573430	+	0.819255i	$0.305612\pi$
$338$	27.2939	1.48459
$339$	−9.25800	−0.502825
$340$	8.37721	0.454318
$341$	4.78215	0.258968
$342$	7.33518	0.396641
$343$	18.1508	0.980053
$344$	17.1907	0.926862
$345$	−14.4728	−0.779190
$346$	20.8597	1.12143
$347$	35.7373	1.91848	0.959239	−	0.282595i	$-0.0911954\pi$
$347$	35.7373	1.91848	0.959239	+	0.282595i	$0.0911954\pi$
$348$	−16.8937	−0.905598
$349$	−15.1078	−0.808701	−0.404351	−	0.914604i	$-0.632502\pi$
$349$	−15.1078	−0.808701	−0.404351	+	0.914604i	$0.632502\pi$
$350$	−3.63312	−0.194199
$351$	−6.24146	−0.333144
$352$	1.19805	0.0638564
$353$	−2.53152	−0.134739	−0.0673696	−	0.997728i	$-0.521461\pi$
$353$	−2.53152	−0.134739	−0.0673696	+	0.997728i	$0.521461\pi$
$354$	16.3326	0.868065
$355$	−10.2382	−0.543389
$356$	34.2856	1.81714
$357$	−2.54080	−0.134473
$358$	−37.6957	−1.99228
$359$	−5.30166	−0.279811	−0.139905	−	0.990165i	$-0.544680\pi$
$359$	−5.30166	−0.279811	−0.139905	+	0.990165i	$0.544680\pi$
$360$	−20.6256	−1.08707
$361$	−17.0297	−0.896301
$362$	21.7048	1.14078
$363$	−0.918445	−0.0482059
$364$	13.7569	0.721060
$365$	−29.5010	−1.54415
$366$	8.21153	0.429224
$367$	9.13428	0.476806	0.238403	−	0.971166i	$-0.423376\pi$
$367$	9.13428	0.476806	0.238403	+	0.971166i	$0.423376\pi$
$368$	−24.2963	−1.26653
$369$	−19.0938	−0.993985
$370$	−40.1661	−2.08814
$371$	−9.94399	−0.516266
$372$	−17.0078	−0.881813
$373$	6.53079	0.338151	0.169076	−	0.985603i	$-0.445922\pi$
$373$	6.53079	0.338151	0.169076	+	0.985603i	$0.445922\pi$
$374$	2.48687	0.128593
$375$	−10.7574	−0.555510
$376$	54.8514	2.82874
$377$	−6.26010	−0.322411
$378$	30.9370	1.59123
$379$	−19.6425	−1.00897	−0.504485	−	0.863421i	$-0.668318\pi$
$379$	−19.6425	−1.00897	−0.504485	+	0.863421i	$0.668318\pi$
$380$	−11.4582	−0.587791
$381$	−1.41082	−0.0722785
$382$	−56.0502	−2.86778
$383$	−28.0869	−1.43517	−0.717586	−	0.696470i	$-0.754753\pi$
$383$	−28.0869	−1.43517	−0.717586	+	0.696470i	$0.754753\pi$
$384$	−18.7288	−0.955752
$385$	5.68260	0.289612
$386$	64.9341	3.30506
$387$	8.17050	0.415330
$388$	24.8650	1.26233
$389$	14.8286	0.751841	0.375921	−	0.926652i	$-0.377327\pi$
$389$	14.8286	0.751841	0.375921	+	0.926652i	$0.377327\pi$
$390$	6.18327	0.313102
$391$	7.67131	0.387955
$392$	−1.21005	−0.0611168
$393$	−1.00752	−0.0508224
$394$	3.87522	0.195231
$395$	23.7025	1.19260
$396$	−8.35052	−0.419629
$397$	0.513142	0.0257539	0.0128769	−	0.999917i	$-0.495901\pi$
$397$	0.513142	0.0257539	0.0128769	+	0.999917i	$0.495901\pi$
$398$	−29.3056	−1.46895
$399$	3.47525	0.173980
$400$	−1.80770	−0.0903848
$401$	33.4550	1.67066	0.835332	−	0.549746i	$-0.185276\pi$
$401$	33.4550	1.67066	0.835332	+	0.549746i	$0.185276\pi$
$402$	−6.69690	−0.334011
$403$	−6.30238	−0.313944
$404$	−60.0648	−2.98834
$405$	−4.46840	−0.222036
$406$	31.0294	1.53996
$407$	−7.86278	−0.389744
$408$	−4.27650	−0.211718
$409$	−2.57499	−0.127325	−0.0636625	−	0.997971i	$-0.520278\pi$
$409$	−2.57499	−0.127325	−0.0636625	+	0.997971i	$0.520278\pi$
$410$	45.2310	2.23380
$411$	−7.73960	−0.381766
$412$	45.0383	2.21888
$413$	−19.7817	−0.973395
$414$	−39.0631	−1.91985
$415$	−33.5824	−1.64850
$416$	−1.57891	−0.0774123
$417$	5.94108	0.290936
$418$	−3.40149	−0.166372
$419$	24.7432	1.20879	0.604393	−	0.796687i	$-0.293416\pi$
$419$	24.7432	1.20879	0.604393	+	0.796687i	$0.293416\pi$
$420$	−20.2103	−0.986161
$421$	−22.4123	−1.09231	−0.546154	−	0.837685i	$-0.683909\pi$
$421$	−22.4123	−1.09231	−0.546154	+	0.837685i	$0.683909\pi$
$422$	20.8678	1.01583
$423$	26.0701	1.26757
$424$	−16.7371	−0.812823
$425$	0.570762	0.0276860
$426$	10.8095	0.523721
$427$	−9.94568	−0.481305
$428$	−59.1928	−2.86119
$429$	1.21042	0.0584394
$430$	−19.3549	−0.933377
$431$	−3.30159	−0.159032	−0.0795161	−	0.996834i	$-0.525338\pi$
$431$	−3.30159	−0.159032	−0.0795161	+	0.996834i	$0.525338\pi$
$432$	15.3930	0.740596
$433$	6.45790	0.310347	0.155174	−	0.987887i	$-0.450406\pi$
$433$	6.45790	0.310347	0.155174	+	0.987887i	$0.450406\pi$
$434$	31.2390	1.49952
$435$	9.19669	0.440948
$436$	−4.57270	−0.218993
$437$	−10.4926	−0.501931
$438$	31.1470	1.48826
$439$	−16.7949	−0.801577	−0.400788	−	0.916171i	$-0.631264\pi$
$439$	−16.7949	−0.801577	−0.400788	+	0.916171i	$0.631264\pi$
$440$	9.56457	0.455973
$441$	−0.575119	−0.0273866
$442$	−3.27744	−0.155892
$443$	−30.6915	−1.45820	−0.729098	−	0.684409i	$-0.760060\pi$
$443$	−30.6915	−1.45820	−0.729098	+	0.684409i	$0.760060\pi$
$444$	27.9641	1.32712
$445$	−18.6646	−0.884788
$446$	13.3907	0.634069
$447$	−6.46528	−0.305797
$448$	25.3495	1.19765
$449$	−1.56946	−0.0740674	−0.0370337	−	0.999314i	$-0.511791\pi$
$449$	−1.56946	−0.0740674	−0.0370337	+	0.999314i	$0.511791\pi$
$450$	−2.90638	−0.137008
$451$	8.85425	0.416930
$452$	39.0334	1.83598
$453$	−4.11695	−0.193431
$454$	17.7464	0.832882
$455$	−7.48908	−0.351094
$456$	5.84930	0.273919
$457$	−34.5254	−1.61503	−0.807516	−	0.589845i	$-0.799189\pi$
$457$	−34.5254	−1.61503	−0.807516	+	0.589845i	$0.799189\pi$
$458$	2.60608	0.121774
$459$	−4.86019	−0.226854
$460$	61.0199	2.84507
$461$	27.4203	1.27709	0.638544	−	0.769585i	$-0.279537\pi$
$461$	27.4203	1.27709	0.638544	+	0.769585i	$0.279537\pi$
$462$	−5.99966	−0.279129
$463$	−3.61913	−0.168195	−0.0840976	−	0.996458i	$-0.526801\pi$
$463$	−3.61913	−0.168195	−0.0840976	+	0.996458i	$0.526801\pi$
$464$	15.4390	0.716736
$465$	9.25880	0.429367
$466$	4.06440	0.188280
$467$	2.56468	0.118679	0.0593397	−	0.998238i	$-0.481100\pi$
$467$	2.56468	0.118679	0.0593397	+	0.998238i	$0.481100\pi$
$468$	11.0051	0.508712
$469$	8.11119	0.374540
$470$	−61.7568	−2.84863
$471$	3.60931	0.166308
$472$	−33.2953	−1.53254
$473$	−3.78885	−0.174212
$474$	−25.0249	−1.14943
$475$	−0.780676	−0.0358199
$476$	10.7125	0.491005
$477$	−7.95488	−0.364229
$478$	26.2872	1.20235
$479$	−2.93213	−0.133973	−0.0669863	−	0.997754i	$-0.521338\pi$
$479$	−2.93213	−0.133973	−0.0669863	+	0.997754i	$0.521338\pi$
$480$	2.31957	0.105873
$481$	10.3623	0.472482
$482$	18.1492	0.826674
$483$	−18.5073	−0.842110
$484$	3.87233	0.176015
$485$	−13.5361	−0.614644
$486$	39.1472	1.77575
$487$	−10.3197	−0.467628	−0.233814	−	0.972281i	$-0.575121\pi$
$487$	−10.3197	−0.467628	−0.233814	+	0.972281i	$0.575121\pi$
$488$	−16.7399	−0.757780
$489$	−12.7673	−0.577358
$490$	1.36239	0.0615464
$491$	−17.6388	−0.796027	−0.398014	−	0.917380i	$-0.630300\pi$
$491$	−17.6388	−0.796027	−0.398014	+	0.917380i	$0.630300\pi$
$492$	−31.4903	−1.41969
$493$	−4.87471	−0.219546
$494$	4.48281	0.201691
$495$	4.54590	0.204323
$496$	15.5432	0.697912
$497$	−13.0923	−0.587269
$498$	35.4562	1.58883
$499$	−26.2776	−1.17635	−0.588175	−	0.808734i	$-0.700153\pi$
$499$	−26.2776	−1.17635	−0.588175	+	0.808734i	$0.700153\pi$
$500$	45.3551	2.02834
$501$	−1.80323	−0.0805625
$502$	−67.1530	−2.99719
$503$	−36.6836	−1.63564	−0.817819	−	0.575475i	$-0.804817\pi$
$503$	−36.6836	−1.63564	−0.817819	+	0.575475i	$0.804817\pi$
$504$	−26.3753	−1.17485
$505$	32.6984	1.45506
$506$	18.1145	0.805287
$507$	10.3446	0.459419
$508$	5.94827	0.263912
$509$	−22.0754	−0.978473	−0.489236	−	0.872151i	$-0.662724\pi$
$509$	−22.0754	−0.978473	−0.489236	+	0.872151i	$0.662724\pi$
$510$	4.81488	0.213207
$511$	−37.7248	−1.66885
$512$	33.3881	1.47556
$513$	6.64766	0.293501
$514$	−24.1242	−1.06407
$515$	−24.5182	−1.08040
$516$	13.4751	0.593209
$517$	−12.0893	−0.531686
$518$	−51.3629	−2.25676
$519$	7.90600	0.347035
$520$	−12.6051	−0.552771
$521$	−26.7323	−1.17116	−0.585581	−	0.810614i	$-0.699133\pi$
$521$	−26.7323	−1.17116	−0.585581	+	0.810614i	$0.699133\pi$
$522$	24.8225	1.08645
$523$	2.28156	0.0997655	0.0498827	−	0.998755i	$-0.484115\pi$
$523$	2.28156	0.0997655	0.0498827	+	0.998755i	$0.484115\pi$
$524$	4.24786	0.185569
$525$	−1.37698	−0.0600964
$526$	41.6747	1.81711
$527$	−4.90763	−0.213780
$528$	−2.98519	−0.129914
$529$	32.8781	1.42948
$530$	18.8441	0.818537
$531$	−15.8248	−0.686736
$532$	−14.6523	−0.635256
$533$	−11.6690	−0.505440
$534$	19.7060	0.852762
$535$	32.2237	1.39315
$536$	13.6522	0.589685
$537$	−14.2870	−0.616528
$538$	6.16765	0.265906
$539$	0.266696	0.0114874
$540$	−38.6594	−1.66364
$541$	−27.4207	−1.17891	−0.589455	−	0.807801i	$-0.700657\pi$
$541$	−27.4207	−1.17891	−0.589455	+	0.807801i	$0.700657\pi$
$542$	7.08951	0.304520
$543$	8.22630	0.353024
$544$	−1.22949	−0.0527138
$545$	2.48931	0.106631
$546$	7.90693	0.338385
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	32.6315	1.39395
$549$	−7.95623	−0.339564
$550$	1.34776	0.0574686
$551$	6.66752	0.284046
$552$	−31.1502	−1.32584
$553$	30.3098	1.28890
$554$	−21.0686	−0.895118
$555$	−15.2233	−0.646192
$556$	−25.0486	−1.06230
$557$	−41.1637	−1.74416	−0.872081	−	0.489362i	$-0.837230\pi$
$557$	−41.1637	−1.74416	−0.872081	+	0.489362i	$0.837230\pi$
$558$	24.9902	1.05792
$559$	4.99331	0.211195
$560$	18.4700	0.780498
$561$	0.942544	0.0397942
$562$	−56.6836	−2.39105
$563$	−41.9675	−1.76872	−0.884360	−	0.466806i	$-0.845405\pi$
$563$	−41.9675	−1.76872	−0.884360	+	0.466806i	$0.845405\pi$
$564$	42.9958	1.81045
$565$	−21.2492	−0.893961
$566$	−60.1215	−2.52710
$567$	−5.71402	−0.239966
$568$	−22.0360	−0.924611
$569$	−15.5916	−0.653636	−0.326818	−	0.945087i	$-0.605976\pi$
$569$	−15.5916	−0.653636	−0.326818	+	0.945087i	$0.605976\pi$
$570$	−6.58569	−0.275844
$571$	−30.3166	−1.26871	−0.634355	−	0.773042i	$-0.718734\pi$
$571$	−30.3166	−1.26871	−0.634355	+	0.773042i	$0.718734\pi$
$572$	−5.10333	−0.213381
$573$	−21.2434	−0.887457
$574$	57.8396	2.41418
$575$	4.15745	0.173378
$576$	20.2788	0.844950
$577$	35.9008	1.49457	0.747285	−	0.664504i	$-0.231357\pi$
$577$	35.9008	1.49457	0.747285	+	0.664504i	$0.231357\pi$
$578$	38.6438	1.60737
$579$	24.6105	1.02278
$580$	−38.7749	−1.61004
$581$	−42.9439	−1.78162
$582$	14.2914	0.592396
$583$	3.68886	0.152777
$584$	−63.4958	−2.62748
$585$	−5.99103	−0.247698
$586$	−24.0985	−0.995501
$587$	8.33164	0.343884	0.171942	−	0.985107i	$-0.444996\pi$
$587$	8.33164	0.343884	0.171942	+	0.985107i	$0.444996\pi$
$588$	−0.948510	−0.0391159
$589$	6.71254	0.276586
$590$	37.4869	1.54331
$591$	1.46874	0.0604158
$592$	−25.5561	−1.05035
$593$	−10.7932	−0.443225	−0.221613	−	0.975135i	$-0.571132\pi$
$593$	−10.7932	−0.443225	−0.221613	+	0.975135i	$0.571132\pi$
$594$	−11.4765	−0.470887
$595$	−5.83171	−0.239077
$596$	27.2588	1.11656
$597$	−11.1070	−0.454580
$598$	−23.8730	−0.976240
$599$	−18.5253	−0.756924	−0.378462	−	0.925617i	$-0.623547\pi$
$599$	−18.5253	−0.756924	−0.378462	+	0.925617i	$0.623547\pi$
$600$	−2.31764	−0.0946174
$601$	44.5411	1.81687	0.908435	−	0.418027i	$-0.137278\pi$
$601$	44.5411	1.81687	0.908435	+	0.418027i	$0.137278\pi$
$602$	−24.7503	−1.00875
$603$	6.48869	0.264240
$604$	17.3578	0.706278
$605$	−2.10804	−0.0857040
$606$	−34.5228	−1.40239
$607$	−22.1435	−0.898775	−0.449388	−	0.893337i	$-0.648358\pi$
$607$	−22.1435	−0.898775	−0.449388	+	0.893337i	$0.648358\pi$
$608$	1.68167	0.0682005
$609$	11.7604	0.476555
$610$	18.8473	0.763106
$611$	15.9324	0.644557
$612$	8.56963	0.346407
$613$	−22.7573	−0.919157	−0.459578	−	0.888137i	$-0.651999\pi$
$613$	−22.7573	−0.919157	−0.459578	+	0.888137i	$0.651999\pi$
$614$	−27.2765	−1.10079
$615$	17.1429	0.691268
$616$	12.2308	0.492794
$617$	−5.65514	−0.227667	−0.113834	−	0.993500i	$-0.536313\pi$
$617$	−5.65514	−0.227667	−0.113834	+	0.993500i	$0.536313\pi$
$618$	25.8862	1.04129
$619$	−8.76926	−0.352466	−0.176233	−	0.984348i	$-0.556391\pi$
$619$	−8.76926	−0.352466	−0.176233	+	0.984348i	$0.556391\pi$
$620$	−39.0368	−1.56775
$621$	−35.4018	−1.42063
$622$	−30.1591	−1.20927
$623$	−23.8676	−0.956235
$624$	3.93417	0.157493
$625$	−21.9098	−0.876393
$626$	7.67682	0.306828
$627$	−1.28919	−0.0514853
$628$	−15.2175	−0.607244
$629$	8.06910	0.321736
$630$	29.6957	1.18311
$631$	−0.148030	−0.00589297	−0.00294649	−	0.999996i	$-0.500938\pi$
$631$	−0.148030	−0.00589297	−0.00294649	+	0.999996i	$0.500938\pi$
$632$	51.0154	2.02929
$633$	7.90907	0.314357
$634$	6.53048	0.259358
$635$	−3.23815	−0.128502
$636$	−13.1195	−0.520222
$637$	−0.351478	−0.0139261
$638$	−11.5108	−0.455716
$639$	−10.4734	−0.414321
$640$	−42.9869	−1.69921
$641$	−11.8264	−0.467115	−0.233557	−	0.972343i	$-0.575037\pi$
$641$	−11.8264	−0.467115	−0.233557	+	0.972343i	$0.575037\pi$
$642$	−34.0216	−1.34273
$643$	−14.1666	−0.558676	−0.279338	−	0.960193i	$-0.590115\pi$
$643$	−14.1666	−0.558676	−0.279338	+	0.960193i	$0.590115\pi$
$644$	78.0300	3.07481
$645$	−7.33566	−0.288841
$646$	3.49074	0.137341
$647$	19.0243	0.747923	0.373962	−	0.927444i	$-0.377999\pi$
$647$	19.0243	0.747923	0.373962	+	0.927444i	$0.377999\pi$
$648$	−9.61745	−0.377809
$649$	7.33831	0.288054
$650$	−1.77621	−0.0696685
$651$	11.8398	0.464039
$652$	53.8293	2.10812
$653$	8.26613	0.323479	0.161739	−	0.986834i	$-0.448290\pi$
$653$	8.26613	0.323479	0.161739	+	0.986834i	$0.448290\pi$
$654$	−2.62820	−0.102771
$655$	−2.31248	−0.0903559
$656$	28.7787	1.12362
$657$	−30.1786	−1.17738
$658$	−78.9722	−3.07866
$659$	−35.7654	−1.39322	−0.696612	−	0.717448i	$-0.745310\pi$
$659$	−35.7654	−1.39322	−0.696612	+	0.717448i	$0.745310\pi$
$660$	7.49728	0.291831
$661$	1.30544	0.0507757	0.0253879	−	0.999678i	$-0.491918\pi$
$661$	1.30544	0.0507757	0.0253879	+	0.999678i	$0.491918\pi$
$662$	−34.0161	−1.32207
$663$	−1.24218	−0.0482421
$664$	−72.2804	−2.80502
$665$	7.97648	0.309315
$666$	−41.0887	−1.59216
$667$	−35.5075	−1.37486
$668$	7.60275	0.294159
$669$	5.07518	0.196218
$670$	−15.3709	−0.593830
$671$	3.68949	0.142431
$672$	2.96618	0.114423
$673$	14.6344	0.564115	0.282057	−	0.959398i	$-0.408983\pi$
$673$	14.6344	0.564115	0.282057	+	0.959398i	$0.408983\pi$
$674$	−51.0188	−1.96517
$675$	−2.63397	−0.101382
$676$	−43.6146	−1.67748
$677$	−8.61393	−0.331060	−0.165530	−	0.986205i	$-0.552934\pi$
$677$	−8.61393	−0.331060	−0.165530	+	0.986205i	$0.552934\pi$
$678$	22.4348	0.861603
$679$	−17.3095	−0.664277
$680$	−9.81554	−0.376409
$681$	6.72604	0.257742
$682$	−11.5885	−0.443748
$683$	6.50361	0.248854	0.124427	−	0.992229i	$-0.460291\pi$
$683$	6.50361	0.248854	0.124427	+	0.992229i	$0.460291\pi$
$684$	−11.7213	−0.448177
$685$	−17.7641	−0.678733
$686$	−43.9847	−1.67934
$687$	0.987723	0.0376840
$688$	−12.3148	−0.469496
$689$	−4.86154	−0.185210
$690$	35.0718	1.33516
$691$	−33.1087	−1.25952	−0.629758	−	0.776791i	$-0.716846\pi$
$691$	−33.1087	−1.25952	−0.629758	+	0.776791i	$0.716846\pi$
$692$	−33.3331	−1.26714
$693$	5.81313	0.220822
$694$	−86.6018	−3.28736
$695$	13.6361	0.517248
$696$	19.7943	0.750300
$697$	−9.08658	−0.344179
$698$	36.6105	1.38573
$699$	1.54044	0.0582647
$700$	5.80560	0.219431
$701$	33.0709	1.24907	0.624535	−	0.780997i	$-0.285288\pi$
$701$	33.0709	1.24907	0.624535	+	0.780997i	$0.285288\pi$
$702$	15.1248	0.570851
$703$	−11.0367	−0.416258
$704$	−9.40375	−0.354417
$705$	−23.4063	−0.881532
$706$	6.13460	0.230879
$707$	41.8135	1.57256
$708$	−26.0988	−0.980854
$709$	−34.6498	−1.30130	−0.650650	−	0.759378i	$-0.725503\pi$
$709$	−34.6498	−1.30130	−0.650650	+	0.759378i	$0.725503\pi$
$710$	24.8102	0.931110
$711$	24.2469	0.909329
$712$	−40.1723	−1.50552
$713$	−35.7474	−1.33875
$714$	6.15709	0.230423
$715$	2.77818	0.103898
$716$	60.2364	2.25114
$717$	9.96306	0.372077
$718$	12.8475	0.479463
$719$	3.76103	0.140263	0.0701315	−	0.997538i	$-0.477658\pi$
$719$	3.76103	0.140263	0.0701315	+	0.997538i	$0.477658\pi$
$720$	14.7754	0.550646
$721$	−31.3529	−1.16764
$722$	41.2679	1.53583
$723$	6.87869	0.255821
$724$	−34.6836	−1.28900
$725$	−2.64184	−0.0981155
$726$	2.22566	0.0826019
$727$	42.9574	1.59320	0.796602	−	0.604505i	$-0.206629\pi$
$727$	42.9574	1.59320	0.796602	+	0.604505i	$0.206629\pi$
$728$	−16.1189	−0.597408
$729$	8.47802	0.314001
$730$	71.4895	2.64595
$731$	3.88827	0.143813
$732$	−13.1217	−0.484993
$733$	32.5724	1.20309	0.601545	−	0.798839i	$-0.294552\pi$
$733$	32.5724	1.20309	0.601545	+	0.798839i	$0.294552\pi$
$734$	−22.1350	−0.817018
$735$	0.516355	0.0190461
$736$	−8.95563	−0.330109
$737$	−3.00896	−0.110836
$738$	46.2699	1.70322
$739$	−30.1478	−1.10900	−0.554502	−	0.832183i	$-0.687091\pi$
$739$	−30.1478	−1.10900	−0.554502	+	0.832183i	$0.687091\pi$
$740$	64.1840	2.35945
$741$	1.69902	0.0624151
$742$	24.0972	0.884635
$743$	27.1034	0.994328	0.497164	−	0.867657i	$-0.334375\pi$
$743$	27.1034	0.994328	0.497164	+	0.867657i	$0.334375\pi$
$744$	19.9280	0.730595
$745$	−14.8393	−0.543669
$746$	−15.8260	−0.579431
$747$	−34.3538	−1.25694
$748$	−3.97393	−0.145301
$749$	41.2064	1.50565
$750$	26.0683	0.951879
$751$	−23.9887	−0.875359	−0.437680	−	0.899131i	$-0.644200\pi$
$751$	−23.9887	−0.875359	−0.437680	+	0.899131i	$0.644200\pi$
$752$	−39.2934	−1.43288
$753$	−25.4515	−0.927505
$754$	15.1700	0.552460
$755$	−9.44933	−0.343896
$756$	−49.4362	−1.79798
$757$	−20.4233	−0.742297	−0.371149	−	0.928573i	$-0.621036\pi$
$757$	−20.4233	−0.742297	−0.371149	+	0.928573i	$0.621036\pi$
$758$	47.5996	1.72889
$759$	6.86553	0.249203
$760$	13.4255	0.486993
$761$	26.0309	0.943619	0.471810	−	0.881701i	$-0.343601\pi$
$761$	26.0309	0.943619	0.471810	+	0.881701i	$0.343601\pi$
$762$	3.41882	0.123851
$763$	3.18324	0.115241
$764$	89.5661	3.24039
$765$	−4.66518	−0.168670
$766$	68.0626	2.45920
$767$	−9.67113	−0.349204
$768$	28.1117	1.01439
$769$	32.7648	1.18153	0.590765	−	0.806844i	$-0.298826\pi$
$769$	32.7648	1.18153	0.590765	+	0.806844i	$0.298826\pi$
$770$	−13.7706	−0.496257
$771$	−9.14325	−0.329286
$772$	−103.762	−3.73449
$773$	−14.4067	−0.518175	−0.259087	−	0.965854i	$-0.583422\pi$
$773$	−14.4067	−0.518175	−0.259087	+	0.965854i	$0.583422\pi$
$774$	−19.7995	−0.711678
$775$	−2.65968	−0.0955386
$776$	−29.1342	−1.04586
$777$	−19.4669	−0.698373
$778$	−35.9340	−1.28830
$779$	12.4284	0.445295
$780$	−9.88064	−0.353784
$781$	4.85676	0.173788
$782$	−18.5898	−0.664770
$783$	22.4960	0.803940
$784$	0.866833	0.0309583
$785$	8.28418	0.295675
$786$	2.44150	0.0870854
$787$	−45.9728	−1.63875	−0.819377	−	0.573254i	$-0.805681\pi$
$787$	−45.9728	−1.63875	−0.819377	+	0.573254i	$0.805681\pi$
$788$	−6.19246	−0.220597
$789$	15.7950	0.562319
$790$	−57.4379	−2.04355
$791$	−27.1727	−0.966149
$792$	9.78426	0.347669
$793$	−4.86236	−0.172668
$794$	−1.24349	−0.0441298
$795$	7.14207	0.253303
$796$	46.8292	1.65982
$797$	−24.0229	−0.850935	−0.425467	−	0.904974i	$-0.639890\pi$
$797$	−24.0229	−0.850935	−0.425467	+	0.904974i	$0.639890\pi$
$798$	−8.42153	−0.298119
$799$	12.4065	0.438911
$800$	−0.666319	−0.0235579
$801$	−19.0933	−0.674629
$802$	−81.0711	−2.86272
$803$	13.9945	0.493856
$804$	10.7014	0.377410
$805$	−42.4784	−1.49717
$806$	15.2725	0.537950
$807$	2.33758	0.0822869
$808$	70.3777	2.47588
$809$	40.7641	1.43319	0.716595	−	0.697490i	$-0.245700\pi$
$809$	40.7641	1.43319	0.716595	+	0.697490i	$0.245700\pi$
$810$	10.8282	0.380465
$811$	−54.1288	−1.90072	−0.950360	−	0.311151i	$-0.899285\pi$
$811$	−54.1288	−1.90072	−0.950360	+	0.311151i	$0.899285\pi$
$812$	−49.5839	−1.74005
$813$	2.68698	0.0942364
$814$	19.0538	0.667835
$815$	−29.3039	−1.02647
$816$	3.06352	0.107245
$817$	−5.31829	−0.186063
$818$	6.23994	0.218174
$819$	−7.66110	−0.267700
$820$	−72.2774	−2.52404
$821$	−52.1354	−1.81954	−0.909768	−	0.415116i	$-0.863741\pi$
$821$	−52.1354	−1.81954	−0.909768	+	0.415116i	$0.863741\pi$
$822$	18.7553	0.654165
$823$	47.7734	1.66528	0.832638	−	0.553817i	$-0.186829\pi$
$823$	47.7734	1.66528	0.832638	+	0.553817i	$0.186829\pi$
$824$	−52.7711	−1.83837
$825$	0.510810	0.0177841
$826$	47.9368	1.66794
$827$	−14.3208	−0.497984	−0.248992	−	0.968505i	$-0.580099\pi$
$827$	−14.3208	−0.497984	−0.248992	+	0.968505i	$0.580099\pi$
$828$	62.4215	2.16930
$829$	33.8554	1.17585	0.587924	−	0.808916i	$-0.299945\pi$
$829$	33.8554	1.17585	0.587924	+	0.808916i	$0.299945\pi$
$830$	81.3799	2.82474
$831$	−7.98515	−0.277002
$832$	12.3932	0.429656
$833$	−0.273694	−0.00948294
$834$	−14.3969	−0.498525
$835$	−4.13883	−0.143230
$836$	5.43546	0.187989
$837$	22.6479	0.782826
$838$	−59.9600	−2.07128
$839$	8.09662	0.279526	0.139763	−	0.990185i	$-0.455366\pi$
$839$	8.09662	0.279526	0.139763	+	0.990185i	$0.455366\pi$
$840$	23.6803	0.817048
$841$	−6.43685	−0.221960
$842$	54.3114	1.87170
$843$	−21.4835	−0.739932
$844$	−33.3461	−1.14782
$845$	23.7432	0.816790
$846$	−63.1753	−2.17201
$847$	−2.69568	−0.0926247
$848$	11.9898	0.411730
$849$	−22.7865	−0.782031
$850$	−1.38312	−0.0474407
$851$	58.7756	2.01480
$852$	−17.2732	−0.591768
$853$	20.7415	0.710176	0.355088	−	0.934833i	$-0.384451\pi$
$853$	20.7415	0.710176	0.355088	+	0.934833i	$0.384451\pi$
$854$	24.1013	0.824728
$855$	6.38093	0.218223
$856$	69.3559	2.37054
$857$	6.04129	0.206367	0.103183	−	0.994662i	$-0.467097\pi$
$857$	6.04129	0.206367	0.103183	+	0.994662i	$0.467097\pi$
$858$	−2.93319	−0.100137
$859$	−5.01431	−0.171086	−0.0855431	−	0.996334i	$-0.527263\pi$
$859$	−5.01431	−0.171086	−0.0855431	+	0.996334i	$0.527263\pi$
$860$	30.9285	1.05465
$861$	21.9217	0.747088
$862$	8.00072	0.272506
$863$	7.10321	0.241796	0.120898	−	0.992665i	$-0.461423\pi$
$863$	7.10321	0.241796	0.120898	+	0.992665i	$0.461423\pi$
$864$	5.67388	0.193029
$865$	18.1461	0.616985
$866$	−15.6494	−0.531787
$867$	14.6463	0.497414
$868$	−49.9187	−1.69435
$869$	−11.2438	−0.381421
$870$	−22.2862	−0.755574
$871$	3.96549	0.134366
$872$	5.35782	0.181439
$873$	−13.8470	−0.468651
$874$	25.4267	0.860071
$875$	−31.5735	−1.06738
$876$	−49.7718	−1.68163
$877$	−8.19348	−0.276674	−0.138337	−	0.990385i	$-0.544176\pi$
$877$	−8.19348	−0.276674	−0.138337	+	0.990385i	$0.544176\pi$
$878$	40.6989	1.37352
$879$	−9.13352	−0.308066
$880$	−6.85168	−0.230970
$881$	21.0986	0.710831	0.355416	−	0.934708i	$-0.384339\pi$
$881$	21.0986	0.710831	0.355416	+	0.934708i	$0.384339\pi$
$882$	1.39368	0.0469277
$883$	41.3137	1.39032	0.695159	−	0.718856i	$-0.255334\pi$
$883$	41.3137	1.39032	0.695159	+	0.718856i	$0.255334\pi$
$884$	5.23723	0.176147
$885$	14.2078	0.477591
$886$	74.3743	2.49865
$887$	10.9280	0.366925	0.183462	−	0.983027i	$-0.441269\pi$
$887$	10.9280	0.366925	0.183462	+	0.983027i	$0.441269\pi$
$888$	−32.7655	−1.09954
$889$	−4.14083	−0.138879
$890$	45.2297	1.51610
$891$	2.11969	0.0710124
$892$	−21.3979	−0.716454
$893$	−16.9693	−0.567857
$894$	15.6672	0.523990
$895$	−32.7918	−1.09611
$896$	−54.9701	−1.83642
$897$	−9.04805	−0.302106
$898$	3.80326	0.126916
$899$	22.7155	0.757605
$900$	4.64430	0.154810
$901$	−3.78565	−0.126118
$902$	−21.4564	−0.714420
$903$	−9.38057	−0.312166
$904$	−45.7352	−1.52113
$905$	18.8812	0.627633
$906$	9.97655	0.331449
$907$	−7.61973	−0.253009	−0.126504	−	0.991966i	$-0.540376\pi$
$907$	−7.61973	−0.253009	−0.126504	+	0.991966i	$0.540376\pi$
$908$	−28.3582	−0.941099
$909$	33.4495	1.10945
$910$	18.1482	0.601607
$911$	11.0538	0.366228	0.183114	−	0.983092i	$-0.441382\pi$
$911$	11.0538	0.366228	0.183114	+	0.983092i	$0.441382\pi$
$912$	−4.19021	−0.138752
$913$	15.9306	0.527228
$914$	83.6651	2.76740
$915$	7.14328	0.236150
$916$	−4.16441	−0.137596
$917$	−2.95711	−0.0976523
$918$	11.7776	0.388720
$919$	25.4030	0.837968	0.418984	−	0.907994i	$-0.362386\pi$
$919$	25.4030	0.837968	0.418984	+	0.907994i	$0.362386\pi$
$920$	−71.4968	−2.35718
$921$	−10.3380	−0.340649
$922$	−66.4472	−2.18832
$923$	−6.40070	−0.210682
$924$	9.58724	0.315397
$925$	4.37303	0.143784
$926$	8.77019	0.288206
$927$	−25.0813	−0.823780
$928$	5.69083	0.186811
$929$	0.877180	0.0287793	0.0143897	−	0.999896i	$-0.495419\pi$
$929$	0.877180	0.0287793	0.0143897	+	0.999896i	$0.495419\pi$
$930$	−22.4368	−0.735730
$931$	0.374353	0.0122689
$932$	−6.49476	−0.212743
$933$	−11.4305	−0.374219
$934$	−6.21497	−0.203360
$935$	2.16335	0.0707492
$936$	−12.8946	−0.421475
$937$	13.5802	0.443646	0.221823	−	0.975087i	$-0.428799\pi$
$937$	13.5802	0.443646	0.221823	+	0.975087i	$0.428799\pi$
$938$	−19.6557	−0.641783
$939$	2.90958	0.0949504
$940$	98.6851	3.21875
$941$	−6.10609	−0.199053	−0.0995265	−	0.995035i	$-0.531733\pi$
$941$	−6.10609	−0.199053	−0.0995265	+	0.995035i	$0.531733\pi$
$942$	−8.74639	−0.284973
$943$	−66.1870	−2.15535
$944$	23.8514	0.776298
$945$	26.9124	0.875459
$946$	9.18148	0.298516
$947$	42.2325	1.37237	0.686187	−	0.727425i	$-0.259283\pi$
$947$	42.2325	1.37237	0.686187	+	0.727425i	$0.259283\pi$
$948$	39.9889	1.29878
$949$	−18.4433	−0.598696
$950$	1.89180	0.0613782
$951$	2.47510	0.0802607
$952$	−12.5517	−0.406804
$953$	18.7654	0.607870	0.303935	−	0.952693i	$-0.401699\pi$
$953$	18.7654	0.607870	0.303935	+	0.952693i	$0.401699\pi$
$954$	19.2770	0.624115
$955$	−48.7585	−1.57779
$956$	−42.0060	−1.35857
$957$	−4.36268	−0.141025
$958$	7.10541	0.229565
$959$	−22.7161	−0.733541
$960$	−18.2068	−0.587621
$961$	−8.13106	−0.262292
$962$	−25.1109	−0.809609
$963$	32.9638	1.06224
$964$	−29.0018	−0.934085
$965$	56.4868	1.81837
$966$	44.8485	1.44298
$967$	−39.6513	−1.27510	−0.637550	−	0.770409i	$-0.720052\pi$
$967$	−39.6513	−1.27510	−0.637550	+	0.770409i	$0.720052\pi$
$968$	−4.53719	−0.145831
$969$	1.32302	0.0425015
$970$	32.8019	1.05321
$971$	−38.9569	−1.25019	−0.625093	−	0.780550i	$-0.714939\pi$
$971$	−38.9569	−1.25019	−0.625093	+	0.780550i	$0.714939\pi$
$972$	−62.5559	−2.00648
$973$	17.4374	0.559016
$974$	25.0075	0.801292
$975$	−0.673195	−0.0215595
$976$	11.9918	0.383848
$977$	27.6929	0.885973	0.442986	−	0.896528i	$-0.353919\pi$
$977$	27.6929	0.885973	0.442986	+	0.896528i	$0.353919\pi$
$978$	30.9389	0.989317
$979$	8.85401	0.282976
$980$	−2.17705	−0.0695432
$981$	2.54649	0.0813032
$982$	42.7439	1.36401
$983$	−39.7200	−1.26687	−0.633436	−	0.773795i	$-0.718356\pi$
$983$	−39.7200	−1.26687	−0.633436	+	0.773795i	$0.718356\pi$
$984$	36.8971	1.17624
$985$	3.37108	0.107412
$986$	11.8128	0.376197
$987$	−29.9311	−0.952717
$988$	−7.16337	−0.227897
$989$	28.3223	0.900596
$990$	−11.0160	−0.350112
$991$	14.2432	0.452452	0.226226	−	0.974075i	$-0.427361\pi$
$991$	14.2432	0.452452	0.226226	+	0.974075i	$0.427361\pi$
$992$	5.72926	0.181904
$993$	−12.8924	−0.409127
$994$	31.7263	1.00630
$995$	−25.4932	−0.808187
$996$	−56.6577	−1.79527
$997$	15.4930	0.490667	0.245334	−	0.969439i	$-0.421103\pi$
$997$	15.4930	0.490667	0.245334	+	0.969439i	$0.421103\pi$
$998$	63.6783	2.01570
$999$	−37.2375	−1.17814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.11	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.11	✓	106	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42329 q^{2} -0.918445 q^{3} +3.87233 q^{4} -2.10804 q^{5} +2.22566 q^{6} -2.69568 q^{7} -4.53719 q^{8} -2.15646 q^{9} +O(q^{10})\)	\(q-2.42329 q^{2} -0.918445 q^{3} +3.87233 q^{4} -2.10804 q^{5} +2.22566 q^{6} -2.69568 q^{7} -4.53719 q^{8} -2.15646 q^{9} +5.10839 q^{10} +1.00000 q^{11} -3.55652 q^{12} -1.31790 q^{13} +6.53241 q^{14} +1.93612 q^{15} +3.25026 q^{16} -1.02624 q^{17} +5.22572 q^{18} +1.40367 q^{19} -8.16302 q^{20} +2.47583 q^{21} -2.42329 q^{22} -7.47517 q^{23} +4.16716 q^{24} -0.556169 q^{25} +3.19364 q^{26} +4.73592 q^{27} -10.4386 q^{28} +4.75007 q^{29} -4.69177 q^{30} +4.78215 q^{31} +1.19805 q^{32} -0.918445 q^{33} +2.48687 q^{34} +5.68260 q^{35} -8.35052 q^{36} -7.86278 q^{37} -3.40149 q^{38} +1.21042 q^{39} +9.56457 q^{40} +8.85425 q^{41} -5.99966 q^{42} -3.78885 q^{43} +3.87233 q^{44} +4.54590 q^{45} +18.1145 q^{46} -12.0893 q^{47} -2.98519 q^{48} +0.266696 q^{49} +1.34776 q^{50} +0.942544 q^{51} -5.10333 q^{52} +3.68886 q^{53} -11.4765 q^{54} -2.10804 q^{55} +12.2308 q^{56} -1.28919 q^{57} -11.5108 q^{58} +7.33831 q^{59} +7.49728 q^{60} +3.68949 q^{61} -11.5885 q^{62} +5.81313 q^{63} -9.40375 q^{64} +2.77818 q^{65} +2.22566 q^{66} -3.00896 q^{67} -3.97393 q^{68} +6.86553 q^{69} -13.7706 q^{70} +4.85676 q^{71} +9.78426 q^{72} +13.9945 q^{73} +19.0538 q^{74} +0.510810 q^{75} +5.43546 q^{76} -2.69568 q^{77} -2.93319 q^{78} -11.2438 q^{79} -6.85168 q^{80} +2.11969 q^{81} -21.4564 q^{82} +15.9306 q^{83} +9.58724 q^{84} +2.16335 q^{85} +9.18148 q^{86} -4.36268 q^{87} -4.53719 q^{88} +8.85401 q^{89} -11.0160 q^{90} +3.55263 q^{91} -28.9463 q^{92} -4.39214 q^{93} +29.2958 q^{94} -2.95899 q^{95} -1.10034 q^{96} +6.42119 q^{97} -0.646282 q^{98} -2.15646 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

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